Data-analytic aspects of the Shiryayev-Roberts control chart: Surveillance of a non-homogeneous Poisson process

Kenett, Ron S.; Pollak, Moshe

doi:10.1080/02664769624413

Cited by 39 publications

(36 citation statements)

References 22 publications

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“…The special data-analytic interpretation of the values of the statistics of methods with a simple relation to the posterior probability is pointed out by Kenett and Pollak (1996). The LR method is optimized for the values of : and < used in the alarm statistic.…”

Section: Minimal Expected Delaymentioning

confidence: 99%

Optimal Surveillance Based on Exponentially Weighted Moving Averages

Frisén¹,

Sonesson²

2006

Sequential Analysis

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Statistical surveillance is used to detect an important change in a process as soon as possible after it has occurred. The EWMA method is used in industry, economics and medicine. Three optimality criteria of surveillance are studied. The ARL criterion violates commonly accepted inference principles and the drawbacks are demonstrated. The ED criterion is based on the minimal expected delay from change to detection. The full likelihood ratio method is optimal according to this criterion. Approximations of this method turn out to be modifications of the EWMA method. The approximations lead to a formula for the optimal value of the smoothing parameter of the EWMA statistic. The usefulness of this formula is shown. It is demonstrated that, for EWMA, the minimax criterion agrees well with that of the ED criterion but not with that of the ARL criterion.

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Section: Minimal Expected Delaymentioning

confidence: 99%

Optimal Surveillance Based on Exponentially Weighted Moving Averages

Frisén¹,

Sonesson²

2006

Sequential Analysis

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“…Hence, ARL 1 is not a good index here. For more literature on CED, see Kenett and Pollak, Zacks and Kenett, Kenett and Zacks, Luceno and Cofino and Frisen …”

Section: Delay To Detectionmentioning

confidence: 99%

On Assessing the Performance of Sequential Procedures for Detecting a Change

Kenett

Pollak

2012

Quality & Reliability Eng

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The literature on statistical process control has focused mostly on the average run length (ARL) to an alarm, as a performance criterion of sequential schemes. When the process is in control, this is the ARL to false alarm, generally denoted by ARL0, and represents the in‐control operating characteristic of the procedure. The ARL from the occurrence of a change to its detection represents an out‐of‐control operating characteristic and is typically embodied by ARL1, the ARL to detection assuming that the change occurs at the very start of surveillance. However, these indices do not tell the whole story, and at times they are not defined well by a single number. We review the role of various operating characteristics in assessing performance of sequential procedures in comparison with ARL0 and ARL1. Copyright © 2012 John Wiley & Sons, Ltd.

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“…In this paper, we shall suppose that δ is fixed. It is clear that the sequence { X n } is a Markov chain which is stationary and homogeneous for n ≤ k = max { j ∈ N ∪ {0} : jδ ≤ τ } and non‐stationary and inhomogeneous for n ≥ k, in general …”

Section: The Modelmentioning

confidence: 99%

Delay in Statistical Control of Systems with Wear

Dohnal

2011

Quality & Reliability Eng

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The target of statistical process control is to identify changes in the behavior of controlled process as quickly as possible. Therefore, as a quality measure of control charts, we use characteristics which quantify the delay between the occurrence of change and its identification by the control chart. The average run length is a commonly used characteristic which does not reflect a real situation. A new characteristic is suggested which is computed in the case of progressive wearing out of the system. We assume several types of progression. The Markov chain approach is used for computation of average delay. Copyright © 2011 John Wiley & Sons, Ltd.

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Data-analytic aspects of the Shiryayev-Roberts control chart: Surveillance of a non-homogeneous Poisson process

Cited by 39 publications

References 22 publications

Optimal Surveillance Based on Exponentially Weighted Moving Averages

Optimal Surveillance Based on Exponentially Weighted Moving Averages

On Assessing the Performance of Sequential Procedures for Detecting a Change

Delay in Statistical Control of Systems with Wear

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